H∞ filters design for fractional-order time-varying delay systems

In this work, the H_∞ filtering problem for fractional-order time-varying-delay systems is investigated. In the absence of disturbances, the observer state x̂(t) should asymptotically converge to the actual state x(t). On the other case, when the system is subject to disturbances, the H_∞ observer must minimize the effect of disturbances on the estimation error. On the basis of the indirect Lyapunov approach [1], the stability condition is given in a Linear Matrix Inequality (LMI) formulation. Finally, a numerical example is presented to illustrate the performances of the proposed observer.